Give the degree measure of θ. Do not use a calculator.
θ...

Question

Give the degree measure of θ. Do not use a calculator.

θ = arcsin (―√3/2)

Accepted Answer

Determine the angle measured theta without using a calculator express the answer in degrees where we have theta equals cos inverse negative two plus cosecant inverse one. And we have four possible answers being 90 degrees, 60 degrees, 30 degrees and negative 60 degrees. I've also included a unit circle on the right side or a reference point or later. No, let's first rewrite our co sequence. We have cos inverse of negative two and go see an inverse of one. We can rewrite these by taking co seeking giving us cos of some angle theta equals negative two in co sequence, some angle theta equals what now to find our angles for data, we need to look at our unit circle. In particular, we need to find where cos is equal to negative two and cos is equals to one. Now, something to mention is the domain of course goes from negative 90 degrees, 90 degrees, except where theta is equal to zero. So theta cannot equal zero degrees. We also know co sequent data S equals to one divided by S sign the. And we know science data on the unic circle is our Y component of our points. Now we just need to find Roo and theta equals negative two and one. Well K and theta equals negative two implies that one divided by sine theta is equals to negative two. So let's see if we can look anywhere on our unit circle where we have something evolving a negative too. Now we did mention that the domain is a negative 90 to 90 degrees. So we are looking only at the right side of our unit circle. Now we have one divided by sine data equals negative two. This kind of implies sign data is equals to negative one half if we were to take the reciprocal of our function. Now, if we look at our unit circle, we can see we have a sign of negative one half at 330 degrees. So theta will be 330 degrees. However, once again, we mentioned our domain with some negative 90 to 90. So we will go counterclockwise and determine our angle is negative 30 degrees. In other words, Kent inverse of negative two is equals to negative 30 degrees. Next, we need to find co sequent data of one. So co sequent the equals one means we have one divided by sine data equals one or sign data equals what? There's only one place where science data is equal to one which occurs at the very top 90 degrees. So we will then say go seeking inverse of one is equals to 90 degrees. Finally, we know that the is equals to cos inverse negative two plus cosecant inverse of one, which based on our calculations, we have negative 30 degrees plus 90 degrees. Giving us an answer of theta equals 60 degrees. If we look at our possible answers, we can determine the answer to our problem is answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Give the degree measure of θ. Do not use a calculator.
θ = arcsin (―√3/2)

Key Concepts

Inverse Trigonometric Functions

Unit Circle

Reference Angles

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